Casio fx-6500P Program Library 2025

Casio fx-6500P Program Library 2025

Last birthday, I reviewed the rare classic, the Casio fx-6500G:

https://edspi31415.blogspot.com/2024/03/spotlight-casio-fx-6500g.html

Parabola Area and Maximum Point: Program P1: Steps 114

Area Under a Parabola set up by the equation:

y = -((x – a)*(x – b)) = -x^2 + p*x – q

p = a + b

q = a * b

Cls

“-((X-A)×(X-B))”

“A”? →A

“B”? → B

A+B → P

AB → Q

-B^3 ÷ 3 + B² P ÷ 2 – Q B + A^3 ÷ 3 - A² P ÷ 2 + Q A → R

“AREA:”

R ◢

“MAX PT:”

P ÷ 2 →X ◢

-((X-A)×(X-B)) → Y

The caret symbol ^ stands for [x^y].

Example:

y = -((x + 4) * (x – 2)) = -x^2 – 2*x + 8

A = -4, B = 2

Area: 36

Maximum Point: (-1, 9)

Circular Sector: Arc Length and Sector Area: Program: P2: Steps: 59

“RADIUS”? →R

“ANG(°)”? → T

RTπ÷180 →L

RL÷2 →A

“ARC LENGTH:”

L ◢

“AREA:”

A

The degree character is generated by the [° ‘ “] key.

Example:

R = 10.5, T (angle) = 120°

Results: Arc length = 21.99114858, Area = 115.45353

Integer Division: Program: P3: Steps: 51

“INT÷”

“X>0”? →X

“M>0”? →M

Int(X÷M)→Q

X-M×Q→R

Q ◢

“REM”

R

Examples:

43 Int÷ 11 = 3 Rem 10

7263 Int÷ 1849 = 3 Rem 1716

Hint: To find out the number of steps in a single program? Simply scroll down the last character and hold down the [ MDisp ] key. Kind of neat because this works outside of programming mode. I think this key was available on most Casio graphing calculators well into the fx-7700G (single G) and fx-9700Gα (E,M,H) series in mid 1990’s.

95% Population Proportion: Program P4: Steps: 96

X successes out of population N

“95 PRCT PROP”

“X”? → X

“N”? → N

X ÷ N → P

√(P(1-P))→ M

1.959963984 M ÷ √N → H

P – H → L

L + 2H → H

“LOW:”

L ◢

“HIGH:”

H

Example:

X = 850, N = 1176

Interval:

LOW: 0.6972058859

HIGH: 0.7483723454

Interval:

Source: HP 21S Stat/Math Calculator: Owner’s Manual. Hewlett Packard. 3^rd Edition. June 1990.

Power Generated by a Wind Turbine: Program P5: Steps: 82

“WIND PWR”

“RADIUS (M)”? →R

“SPEED (M÷S)”? → V

“DENSITY”? →P

π × R² × P × V^3 ÷ 2 → W

“POWER:”

W

Example:

R = 8.18 m, V = 4.48 m/s, P = 1.2 kg/m³

Result: 11340.74989 W

Source: Sharp Electronics Corporation Conquering The Sciences: Applications for the SHARP Scientific Calculator EL-506A Sharp Corporation. Osaka, Japan. 1986. pp.75-77

Round to Nearest Integer (display only): Program P6: Steps: 11

?→N

Fix 0

Rnd

Norm

Examples:

N = 19.273 → 19

N = 44.8273 → 45

N = -2.82 → -3

That’s it. I wish you all a wonderful day. Thank you,

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

hp 9g: Sample Programs

hp 9g:  Sample Programs

Introduction

As I mentioned in yesterday's blog, today's blog will have some sample programs for the hp 9g.   

The hp 9g's programming language is a mix of C and Basic, and is unique from the rest of the Hewlett Packard calculators.    The hp 9g has 400 steps of programming memory to be allocated among 10 program files, P0 through P9.   

The 9g has 26 variables, but can be extended up to 53 variables at the cost of program steps.  The square brackets indicate indirect addressing.  The number in the square brackets is the number of steps away from the variable.   Any variable beyond Z (Z[0], A[25]) must be addressed in this fashion.  

Example: 

A[0] calls up A

A[1] calls up B

...

A[25] calls up Z. 

We can use any letter, but I recommend using either A or Z. 

hp 9g Program:  Integer Division

This program gives the quotient and remainder of N ÷ D.  The program here assumes you enter positive integers, and some code can be entered for checking inputs.  

INPUT N

INPUT D

Q=INT(N/D)

R=N-Q*D

PRINT Q," R",R

END

Examples:

N = 4379, D = 8;  Result:  547 R3

N = 5884, D = 29;  Result:  202 R26

Note:  The PRINT command converts variable values to strings automatically, without the need for a string or STR$ command.

hp 9g Program:  Arithmetic-Geometric Mean

This program determines the AGM given two numbers A and G.

INPUT A

INPUT B

PRINT "ACC. 10^-8"

Lbl 0:

X=.5(A+G)

Y=√(AG)

If (ABS(X-Y)<10^(-8))

Then {Goto 1}

A=X

G=Y

Goto 0

Lbl 1:

Print "ANS= ", X

Examples:

A = 1.3, G = 1.5,   Result:  ANS ≈ 1.39821143

A = 20, G = 45,  Result:  ANS ≈ 31.23749374

Notes:  

10^ is from [ 2nd ] (10^x) the antilog function.

The label command must have the colon character after the label number, or a syntax error occurs.  

If you run a program from the Main mode by the [ PROG ] key, you will be transferred to Program mode when the program finishes.

hp 9G Program: The Maximum Value of A through X

Y = maximum value

Z = counter variable

PRINT "MAX(A:X)"; ◢

FOR(Z=2;Z<23;Z++){

IF(A[Z]>Y)

THEN{Y=A[Z]}};

PRINT "MAX=",Y;

END

Example:  

Clear all variable in the MAIN mode by CL-VAR

Set up variables: 

A = 12, D = 24, E = 37, G = 40, S = 19, T = 16, U = 7

Result:  MAX= 40

Notes:   

++ is from the Instruction menu, it is a smaller-jointed double plus.

When the program encounters a run/stop instruction (◢), the last message is displayed.  Continue execution by pressing the equals key [ = ].  

hp 9g Program:  Plotting y = A * sin(B * x + C) + D

The programming mode does not offer a lot of support when it comes to graphs.  

PRINT "SINE"

SLEEP(.5)

INPUT A,B,C,D

RANGE(-2π,2π,π/4,-A,A,1)

Graph Y=A*sin(BX+C)+D

PRINT "PRESS G<>T"

END

A = 1, B = 1, C = 0, D = 0

Notes:

Prior to running the program, set the angle mode to Radians through the [DRG] key.  Also, press [ 2nd ] [ → ] (CLS) to clear the graph screen.  Unfortunately, neither of these commands can be programmed.  

Plots from programs cannot be traced.

When the program ends, you will need to switch to Main mode, press [G<>T] to show the graph.   Not a very efficient way of showing a graph.  

That is a sample of the programs for the hp 9g.  Good for number crunching, kind of a little bit to be desired for graphics.

Until next time,

Eddie 

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Retro Review: Casio fx-55 Fraction Mate

 Retro Review: Casio fx-55 Fraction Mate

Quick Facts

Model: fx-55 Fraction Mate

Company: Casio

Years: probably the 1990s or early 2000s, predecessor to the fx-55 Plus* 

Memory Register:  1 independent memory

Battery:  Solar with battery back up (LR44)

Screen:  8 digits, 4 digit numerator, 4 digit denominator, function indicator (+, -, ×, ÷, ^), equals and parenthesis indicators 

Logic:  Algebraic

Comes with hard case and reference card  

In 2018, I reviewed the fx-55 Plus:  https://edspi31415.blogspot.com/2018/08/review-casio-fx-55-plus.html

Right now there are plenty of fx-55 (original keyboard) for sale on auction sites for eBay at really inexpensive prices, sometimes as low as about $2.00.

Target Audiences

*  Elementary and middle school students

*  Anyone who wants a few more functions than a regular four-function calculator, but not a scientific calculator

*  You want a calculator with an emphasis on fractions

Keyboard

The fx-55 Fraction Mate does not have a shift key.   Some of the keys are:

[ + ], [ - ], [ × ], [ ÷ ]:  Arithmetic keys

[ ( ], [ ) ]:  Parenthesis keys

[ x^y ]:  Power key with a caret indicator on the screen

[ 1/x ]:  Reciprocal

[ RAN# ]:  3 digit random number between 0 and 1

[ FIX ]:  Fix setting.  For float setting, press [ FIX ] [ . ]

[ RND ]:  Round number to fixed setting internally

[ 10^x ]:  Antilog function

[ X ←→ Y ]:  Switch operators

[ X ←→ M]:  Exchange number in the display with number in memory

[ % ]: Percent key, see below

[ > ]: Backspace key

[ a ], [ b/c ]:  Fraction entry keys

[ F ←→ D ]:  Fraction/decimal conversion

[ a b/c ←→ d/c ]:  Improper/proper fraction conversion

[ SIMP ]:  Fraction simplification key

[ ÷R ]:  Integer division, with quotient and remainder.  If both numbers are positive, then remainder acts as a modulo operator

[ √ ]: square root

[ x^2 ]: square function

Integer Division

Pressing [ ÷R ] will return both the quotient and remainder of a division calculation.  If both numbers are positive, then the remainder is the modulo.  

Example:  55 [ ÷R ] 12 returns 4 R 7.  Then 55 = 7 MOD 12.

Percent Key

To add % to n, press:

n [ × ] p [ % ] [ + ]

To subtract % from n, press:

n [ × ] p [ % ] [ - ]

Simplify Key

The [ SIMP ] key simplifies fractions when possible.   The factor used to simplify the fraction is briefly displayed.  All fractions on the fx-55 FRACTION MATE are simplified manually.

Example:   1450/2900 = 

1450 [ b/c ] 2900 [ = ]

Display:  = 1450/2900  Simp

The Simp indicator means the fraction can be simplified.

[ SIMP ]

2 brifely displays before 725/1450 Simp

Repeated presses of [ SIMP ]:

5,  145/290 Simp

5,  29/58  Simp

29,  1/2

Order of Operations

The fx-55 follows the order of operations.  This is great for students in algebra.  

Example: 

3 [ + ] 9 [ × ] 11 [ = ] returns 102     (multiplication/division first, then addition/subtraction) 

Verdict

I like the fx-55 Fraction Mate.  It has a lot of additional functions that beyond the traditional four-function calculator:  parenthesis, powers, reciprocal, fractions.  The display and the numbers are big.  I like how the arithmetic and power functions are displayed.   Worth the buy.

Casio Ledudu's page for fx-55, including the manual:  https://casio.ledudu.com/pockets.asp?type=1176&lg=eng

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

HP 12C Platinum: Finding the Day of Easter

HP 12C Platinum:  Finding the Day of Easter

An Easter Algorithm

One can figure out when Easter is by the following algorithm:

“  c = y / 100

    n = y - 19 * ( y / 19 )

    k = ( c - 17 ) / 25

    i = c - c / 4 - ( c - k ) / 3 + 19 * n + 15

    i = i - 30 * ( i / 30 )

    i = i - ( i / 28 ) * ( 1 - ( i / 28 ) * ( 29 / ( i + 1 ) )

        * ( ( 21 - n ) / 11 ) )

    j = y + y / 4 + i + 2 - c + c / 4

    j = j - 7 * ( j / 7 )

    l = i - j

    m = 3 + ( l + 40 ) / 44

    d = l + 28 - 31 * ( m / 4 )

“  (see the Source below, http://aa.usno.navy.mil/faq/docs/easter.php )

The only input is y, the four digit year (1997, 2015, etc).   Each of the slashes “/” in the above text refers to integer division.  Hence in this case:  a/b refers to INTG(a ÷ b).

Other things I noticed while porting this algorithm to the HP 12C Platinum:

The line y - 19 * ( y / 19 ) can be expressed as y MOD 19 and 19 * fPart(y ÷ 19).   This happens in three other lines (2^nd, 5^th, and 8^th).  See how to calculate the MOD function, when both arguments are positive on the HP 12C here:  http://edspi31415.blogspot.com/2016/07/hp-12c-programming-part-i-modulus-gcd.html

On the HP 12C Platinum, the LSTx function moved to [ g ] [ + ].  (Code 43, 40)

After the 5^th line, the variable i will between 0 and 29.  If i ≤ 27, the 6^th line can be skipped entirely since iPart(i/28) = 0.  Otherwise, iPart(i/28) = 1.  This cuts on down the number of steps needed.

I was also to combine some steps in the beginning by computing c and k while building i at the same time.

Storage arithmetic is allowed on R0 – R4 on both the HP 12C Platinum and the classic HP 12C.  By the way, the reason why I mention the HP 12C Platinum is that this program is 133 steps.  Only 99 steps are possible on the classic HP 12C.

Store registers:

R0: four digit year

R1:  c, m (result: month)

R2:  n, j, d (result: day)

R3: k, l

R4: i

Instructions:  Enter the four digit year.  Press [ R/S ].  The month will be displayed (stored in R1).  Press [ R/S ] to get the day (stored in R2).

HP12C Platinum Program:  Easter

STEP	CODE	KEY	Notes
001	44, 0	STO 0	Store year (y)
002	1	1
003	25	%
004	43, 25	INTG
005	44, 1	STO 1	Store c
006	44, 4	STO 4	Start i
007	36	ENTER	To fill the stack
008	36	ENTER
009	4	4
010	10	÷
011	43, 25	INTG
012	44, 30, 4	STO- 4
013	33	R↓
014	36	ENTER
015	36	ENTER
016	1	1
017	7	7
018	30	-
019	2	2
020	5	5
021	10	÷
022	43, 25	INTG
023	44, 3	STO 3	Store k
024	30	-
025	3	3
026	10	÷
027	43, 25	INTG
028	44, 30, 4	STO- 4
029	1	1
030	5	5
031	44, 40, 4	STO+ 4
032	45, 0	RCL 0
033	1	1
034	9	9
035	10	÷
036	43, 40	LSTx	LSTx is [ g ] [ + ] on the Platinum
037	34	X<>Y
038	43, 24	FRAC
039	20	*	y MOD 19
040	44, 2	STO 2	Store n
041	1	1
042	9	9
043	20	*
044	44, 40, 4	STO+ 4
045	45, 4	RCL 4
046	3	3
047	0	0
048	10	÷
049	43, 40	LSTx
050	34	X<>Y
051	43, 24	FRAC
052	20	*
053	44, 4	STO 4	i MOD 30
054	2	2
055	7	7
056	45, 4	RCL 4
057	43, 44	x≤y	Is i≤27?
058	43, 33, 080	GTO 080	If so, go to step 080
059	2	2
060	9	9
061	45, 4	RCL 4
062	1	1
063	40	+
064	10	÷
065	43, 25	INTG
066	20	*
067	1	1
068	34	X<>Y
069	30	-
070	2	2
071	1	1
072	45, 2	RCL 2
073	30	-
074	1	1
075	1	1
076	10	÷
077	43, 25	INTG
078	20	*
079	44, 30, 4	STO- 4
080	45, 0	RCL 0
081	45, 2	STO 2	Start j
082	4	4
083	10	÷
084	43, 25	INTG
085	44, 40, 2	STO+ 2
086	45, 4	RCL 4
087	2	2
088	40	+
089	45, 1	RCL 1
090	30	-
091	44, 40, 2	STO+ 2
092	45, 1	RCL 1
093	4	4
094	10	÷
095	43, 25	INTG
096	44, 40, 2	STO+ 2
097	45, 2	RCL 2
098	7	7
099	10	÷
100	43, 40	LSTx
101	34	X<>Y
102	43, 24	FRAC
103	20	*
104	44, 2	STO 2	j MOD 7
105	45, 4	RCL 4
106	34	X<>Y
107	30	-
108	44, 3	STO 3	Store l
109	4	4
110	0	0
111	40	+
112	4	4
113	4	4
114	10	÷
115	43, 25	INTG
116	3	3
117	40	+
118	44, 1	STO 1	Store month (m)
119	31	R/S	Displays m
120	4	4
121	10	÷
122	43, 25	INTG
123	3	3
124	1	1
125	20	*
126	16	CHS
127	2	2
128	8	8
129	40	+
130	45, 3	RCL 3
131	40	+
132	44 , 2	STO 2	Store day (d)
133	43, 33, 000	GTO 000	Stop, display d

Examples and Test Data:

2016: 3, 27

Keystrokes:  2016 [R/S] [R/S]

1995: 4, 16

2124: 4, 2

1977: 4, 10

2017: 4, 16

1826: 3, 26

These results have been verified. 

Now we can determine when is Easter at any year.  Happy Easter in advance!

Eddie

Source:    The United States Naval Observatory  “The Date of Easter”  March 11, 2016.  http://aa.usno.navy.mil/faq/docs/easter.php  Retrieved September 2, 2016

This blog is property of Edward Shore, 2016.